Combining log-homotopy flow with tensor decomposition based solution for Fokker-Planck equation

The optimal non-linear filter estimates can be obtained by solving the Fokker-Planck equation (FPE) for the time propagation, together with the Bayesian measurement inclusion. An issue faced when solving the FPE is the curse of dimensionality. Recently, a tensor based approach has been proposed, which is said to be suitable for high dimensional problems. Then Bayesian measurement inclusion also presents challenges of its own, e.g. particle degeneracy in case of particle filtering. A class of methods known as particle flow filters make use of the gradual inclusion of measurements to alleviate this problem. In this work, we combine these two methods in a tensor based framework and provide a recursive filtering solution. This involves solving the FPE for both propagation and measurement update steps. It is shown that this method outperforms the standard EKF and achieves near optimal estimation accuracy.